The Student Room Group

Probability

I'm stuck on this question:

For married couples the probability that the husband has passed his driving test is 7/10 and the probability that the wife has passed her driving test is 1/2. The probability that the husband has passed, given that the wife has passed is 14/15.

I've found by doing the other questions that the probability that, for a random chosen married couple, the driving test will have been passed by

a) both of them - is 7/15
b) only one of them - is 4/15
c) neither of them - is 4/15

I'm not sure how to do this part of the question though:

If two married couples are chosen at random, find the probability that only one of the husbands and only one of the wives will have passed the driving test. The answer in the book is 119/450, but I really don't know how to get it.

Thanks very much for your help.
sweet_gurl


If two married couples are chosen at random, find the probability that only one of the husbands and only one of the wives will have passed the driving test. The answer in the book is 119/450, but I really don't know how to get it.

Thanks very much for your help.


Prob. of man only = 1/2 -7/15 = 1/30

Prob of woman only = 7/10 - 7/15 = 7/30

Therefore, total probability of one man and one woman = Probability of a couple passing and neither of the other two passing x2 (works for either couple) = 7/15 x 4/15 x 2 = 112/450

+

Probability a man from one couple and a woman from another couple pass

= 2 x(1/30 x7/30) = 14/900 = 7/450

Add them together to give 119/450
Reply 2
KAISER_MOLE
Prob. of man only = 1/2 -7/15 = 1/30

Prob of woman only = 7/10 - 7/15 = 7/30

Therefore, total probability of one man and one woman = Probability of a couple passing and neither of the other two passing x2 (works for either couple) = 7/15 x 4/15 x 2 = 112/450

+

Probability a man from one couple and a woman from another couple pass

= 2 x(1/30 x7/30) = 14/900 = 7/450

Add them together to give 119/450


Thank you very much! :smile: